On quaternion algebra over the composite of quadratic number fields and over some dihedral fields

TL;DR

This paper characterizes quaternion division algebras over composite quadratic number fields and certain dihedral fields, providing a comprehensive understanding of their algebraic structure in these contexts.

Contribution

It offers a complete characterization of quaternion division algebras over composite quadratic and specific dihedral number fields, extending existing algebraic classifications.

Findings

Characterization of quaternion division algebras over composite quadratic fields

Extension of classification to some dihedral fields

Provides criteria for algebra division properties

Abstract

Let p and q be two positive primes. In this paper we obtain a complete characterization of quaternion division algebras H_K(p,q) over the composite K of n quadratic number fields. Also, in Section 6, we obtain a characterization of quaternion division algebras H_K(p,q) over some dihedral fields K.